Branzino, also called European sea bass, is a delicate white fish with a slightly sweet, nutty taste.
Rub each fish inside and out with some of the oil, and season inside with salt and pepper. Arrange about 4 lemon slices and 2 thyme sprigs in each cavity. Tie fish loosely with kitchen twine. Tuck 3 bay leaves under twine.
Toss tomatoes, endives, fennel, 2 tablespoons oil, salt, and pepper in a cast-iron skillet (if crowded, cook in batches).
Preheat grill to medium. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 5 or 6 seconds.) Place skillet on grill, and cook, stirring once or twice, until vegetables are tender and caramelized, about 12 minutes. At the same time, place fish on grill rack, and cook, flipping once, until opaque, 5 to 6 minutes per side. Drizzle fish and vegetables with oil, and serve with lemon wedges for squeezing.
Soak fish in cold water for 30 minutes before using to prevent it from burning on the grill. Instead of cooking the fish directly on the grill rack, you can cook each in a cast-iron skillet placed on the grill.